Unfolding a composed ensemble of energy spectra using singular value decomposition

In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectra belong to an ensemble where there are large realization-to-realization fluctuations the canonical methods for unfolding fail. Here we show that singular value decomposition can be used even for the challenging situations where the ensemble is composed out of realizations originating from a different range of parameters resulting in a non-monotonous local density of states. This can be useful in experimental situations for which the physical parameters cannot be tightly controlled, or for situations for which the local density of states is strongly fluctuating.